Differential inequalities and boundary problems for functional-differential equations

1973 ◽  
pp. 41-53 ◽  
Author(s):  
L. J. Grimm ◽  
L. M. Hall
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Differential Inequalities ◽  
Boundary Problems ◽  
Functional Differential

Upper and Lower Solutions of Boundary Value Problems for Functional Differential Equations and Theorems on Functional Differential Inequalities

2000 ◽  
Vol 7 (3) ◽  
pp. 489-512 ◽  
Author(s):  
R. Hakl ◽  
I. Kiguradze ◽  
B. Půža
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Differential Inequalities ◽  
Bounded Operators ◽  
Nonlinear Operators ◽  
Functional Differential

Abstract Sufficient conditions are found for the existence of an upper and a lower solutions of the boundary value problem where and are linear bounded operators, and and are continuous, generally speaking nonlinear, operators. Kamke type theorems are proved on functional differential inequalities.

Multi-point boundary value problems for linear functional-differential equations

2017 ◽  
Vol 24 (2) ◽  
pp. 193-206
Author(s):  
Alexander Domoshnitsky ◽  
Robert Hakl ◽  
Bedřich Půža
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Linear Functional ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Differential Inequalities ◽  
Point Boundary ◽  
Functional Differential

AbstractEfficient conditions guaranteeing the solvability of multi-point boundary value problems for linear functional-differential equations are established in this paper. The results are proved using the theorems on functional-differential inequalities.

scholarly journals Differential inequalities for hysteresis systems

1996 ◽  
Vol 9 (4) ◽  
pp. 459-468 ◽  
Author(s):  
Vladimir V. Chernorutskii ◽  
Mark A. Krasnosel'skii
Keyword(s):  
Differential Equations ◽  
State Space ◽  
Differential Inequality ◽  
Functional Differential Equations ◽  
The State ◽  
Differential Inequalities ◽  
Functional Differential

The theory of differential inequalities is extended to functional-differential equations with hysteresis nonlinearities. A key feature is the existence of a semiorder of the state space of nonlinearity and a special monotonicity of the righthand side of differential inequality.This article is dedicated to the memory of Roland L. Dobrushin.

Almost Periodicity and Lyapunov's Functions for Impulsive Functional Differential Equations with Infinite Delays

2010 ◽  
Vol 53 (2) ◽  
pp. 367-377 ◽  
Author(s):  
Gani Tr. Stamov
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
Continuous Functions ◽  
Differential Inequalities ◽  
Almost Periodic ◽  
Infinite Delays ◽  
Piecewise Continuous ◽  
Functional Differential

AbstractThis paper studies the existence and uniqueness of almost periodic solutions of nonlinear impulsive functional differential equations with infinite delay. The results obtained are based on the Lyapunov–Razumikhin method and on differential inequalities for piecewise continuous functions.

scholarly journals A comparison theorem for functional differential equations

1976 ◽  
Vol 14 (3) ◽  
pp. 343-347 ◽  
Author(s):  
Athanassios G. Kartsatos ◽  
Hiroshi Onose
Keyword(s):  
Differential Equations ◽  
Comparison Theorem ◽  
Functional Differential Equations ◽  
Differential Inequalities ◽  
Open Problems ◽  
Ordinary Case ◽  
Functional Differential ◽  
Image Position

In this paper, we study the oscillation of nth-order differential equations. Recently, Atkinson and the present authors studied (separately) the comparison properties of differential inequalities. Kartsatos treated the nth-order ordinary case and proposed several open problems.The purpose of this paper is to answer one of them in the affirmative concerning more general functional differential equations. The result is that if under several conditions, the equationis oscillatory for n even or a solution x(t) of (1) is oscillatory or for n odd, then this is also the case for the equation

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